Long Chen. University of California at Irvine and Peking University

Abstract: The first order condition of the constrained minimization problem leads to a saddle point problem. A multigrid method using a multiplicative Schwarz smoother for saddle point problems can thus be interpreted as a successive subspace optimization method based on a multilevel decomposition of the constraint space. Convergence theory is developed for successive subspace optimization methods based on two assumptions on the space decomposition: stable decomposition and strengthened Cauchy-Schwarz inequality, and successfully applied to the saddle point systems arising from mixed finite element methods for Poisson, Stokes equations, and plate bending problems. Uniform convergence is obtained without the full regularity assumption of the underlying partial differential equations. Exact sequences of Hilbert complexes plays an important role in the design and analysis of our method.  

报告时间：2015年12月24日16:00-17:00pm

报告地点：数学科学研究院316会议室（环境学院楼316）